A benders stochastic decomposition approach for the optimization under uncertainty of inventory control considering periodic review policy

This paper presents the application of a decomposition scheme for a problem of inventory control of one echelon, one item, uncertain demand and based on a (R, S) replacement policy using twostage stochastic programming, as originally proposed by Cunha et al. (2014). We proposed two methodologies, one based on L-shaped (Van Slyke & Wets, 1969), and the other, based on multicut L-shaped (Birge & Louveaux, 1988), for accelerating the computational solution process. The results showed that both proposed methodologies are capable to satisfactorily improve the solution process in terms of computational time. However, despite the fact that the single-cut method always required more iterations than the multi-cut version to obtain optimal solutions, the single-cut presented better performance in terms of computational time, especially when large number of scenarios and periods are considered.